Is it a commission? A real estate service fee? Or a finder's fee?

We all know we need to have a buyer's rep agreement signed but what about when you're representing the seller by listing their home and they're also looking for a new home to buy? I've often agreed to a reduced commission in the scenario where I'll be listing the home AND acting as the buyer's agent for their new home transaction. I always put that in writing in the listing agreement. All my agents do the same. And I've assumed because of the great relationship we've developed while listing their house, there's no need to have my clients sign a separate buyer's representation agreement. Live and learn. On two separate occasions, once with my direct client - once with one of my agent's clients, we've listed the house (even sold the house) only to be notified that our client (now the buyer) has gone out, on their own, and found their new home. "No need to have you involved as we found the house". Hmmmm, never mind that I/we've already spent hours looking for the new home, never mind that I've spent countless hours without the client ruling out home after home - they "found" the home on their own.  Fortunately, I had already sold my clients home when it happened to me so I was able to say to them "Hmmmm, I believe you're confusing my real estate services fees with a "finder's fee" - felt very satisfying to say but I still didn't collect the buyer's agent commission. Unfortunately, one of my agents is currently in this same situation and has not yet sold the home. We were, however, able to point out that the listing agreement provided for a reduced listing commission only in the event that we served as their buyer's agent. Further reinforcement that everything has to be in writing.  Never assume anything.